Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Arbitrarily long factorizations in mapping class groups
Date
2015-05-12
Author
Korkmaz, Mustafa
Metadata
Show full item record
Item Usage Stats
180
views
0
downloads
Cite This
On a compact oriented surface of genus g with n ≥ 1 boundary components, δ1, δ2, ..., δn, we consider positive factorizations of the boundary multitwist tδ1 tδ2 ...tδn, where tδi is the positive Dehn twist about the boundary δi. We prove that for g ≥ 3, the boundary multitwist tδ1 tδ2 can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for g ≥ 8. This fact has immediate corollaries on the Euler characteristics of the Stein fillings of conctact three manifolds.
URI
http://at.yorku.ca/c/b/k/j/81.htm
https://hdl.handle.net/11511/70955
Conference Name
49th Spring Topology and Dynamics Conference 2015 (14-16 May 2015)
Collections
Department of Mathematics, Conference / Seminar
Suggestions
OpenMETU
Core
Arbitrarily Long Factorizations in Mapping Class Groups
DALYAN, ELİF; Korkmaz, Mustafa; Pamuk, Mehmetcik (2015-01-01)
On a compact oriented surface of genus g with n= 1 boundary components, d1, d2,..., dn, we consider positive factorizations of the boundary multitwist td1 td2 tdn, where tdi is the positive Dehn twist about the boundary di. We prove that for g= 3, the boundary multitwist td1 td2 can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn- Morris, who proved this result for g= 8. This fact has immed...
Surface mapping class groups are ultrahopfian
Korkmaz, Mustafa (2000-07-01)
Let S denote a compact, connected, orientable surface with genus g and h boundary components. We refer to S as a surface of genus g with h holes. Let [Mscr ]S denote the mapping class group of S, the group of isotopy classes of orientation-preserving homeomorphisms S → S. Let G be a group. G is hopfian if every homomorphism from G onto itself is an automorphism. G is residually finite if for every g ∈ G with g ≠ 1 there exists a normal subgroup of finite index in G which does not contain g. Every finitely ...
Automorphisms of curve complexes on nonorientable surfaces
Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01)
For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
Automorphisms of complexes of curves on odd genus nonorientable surfaces
Atalan Ozan, Ferihe; Korkmaz, Mustafa; Department of Mathematics (2005)
Let N be a connected nonorientable surface of genus g with n punctures. Suppose that g is odd and g + n > 6. We prove that the automorphism group of the complex of curves of N is isomorphic to the mapping class group M of N.
On the moduli of surfaces admitting genus 2 fibrations
Onsiper, H; Tekinel, C (Springer Science and Business Media LLC, 2002-12-01)
We investigate the structure of the components of the moduli space Of Surfaces of general type, which parametrize surfaces admitting nonsmooth genus 2 fibrations of nonalbanese type, over curves of genus g(b) greater than or equal to 2.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Korkmaz, “Arbitrarily long factorizations in mapping class groups,” presented at the 49th Spring Topology and Dynamics Conference 2015 (14-16 May 2015), Bowling Green State University Bowling Green, OH, USA, 2015, Accessed: 00, 2021. [Online]. Available: http://at.yorku.ca/c/b/k/j/81.htm.